We analyse the behaviour of the Dirac field under the effects of the violation of the Lorentz symmetry determined by a fixed time-like vector background and azimuthal electric fields. We show, from the interaction of the Dirac particle with an azimuthal electric field (proportional to the inverse of the radial distance) and the fixed time-like vector field, that analogues of the Aharonov-Bohm effect can be obtained. Besides, from the interaction of the Dirac field with an azimuthal electric field (proportional to the radial distance) and the fixed time-like vector field, therefore, a relativistic analogue of the Landau quantization can be achieved.

中文翻译：

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Aharonov-Bohm 效应和 Landau 量子化的相对论类比，洛伦兹对称违反由方位角电场和固定矢量场确定

我们分析了在由固定的类时矢量背景和方位角电场确定的洛伦兹对称性破坏的影响下狄拉克场的行为。我们表明，从 Dirac 粒子与方位角电场（与径向距离的倒数成正比）和固定的类时矢量场的相互作用，可以获得 Aharonov-Bohm 效应的类似物。此外，通过狄拉克场与方位角电场（与径向距离成正比）和固定类时矢量场的相互作用，可以实现朗道量化的相对论模拟。